Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 5 min ago
PreprintCC BY 4.0arXiv

The Discrete Monotonicity Property in Rank Two

  • Fei Xue
Open at sourcePDFDOICite

Abstract

The Betke--Henk--Wills conjecture predicts a bound for lattice-point counts in terms of successive minima. Malikiosis introduced the discrete monotonicity property for normalized residue counts as a sufficient condition for this bound and its extension to nonsymmetric convex bodies. We prove that every compact convex set satisfies this property for lattice subgroups of rank at most two, in arbitrary ambient dimension.

Related

  1. Monotonicity Property of Non-Archimedean Heat Equation
    Alexandra V. Antoniouk, Anatoly N. Kochubei
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. On the Monotonicity of Discrete Entropy for Log-Concave Random Vectors on ℤd
    Matthieu Fradelizi, Lampros Gavalakis, Martin Rapaport
    HALPreprintCC BY-NC-ND 4.0Full textGeneral mathematicsHAL
  3. Characterizing the Daugavet property by squares of rank-one operators
    Johann Langemets
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. A Complementarity Property of Rank-One Multiplicative Maps
    K. C. Sivakumar
    arXivPreprintCC0Full textOptimisation & controlarXiv
  5. On a certain system of discrete equations with the Laurent property
    Andrei K. Svinin
    arXivPreprintCC BY 4.0Full textMathematical physicsStatistical & nonlinear physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{xue2026discrete,
  title = {{The Discrete Monotonicity Property in Rank Two}},
  author = {Fei Xue},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39026},
  eprint = {2610.39026},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39026},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Discrete Monotonicity Property in Rank Two
AU  - Fei Xue
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.39026
UR  - https://arxiv.org/abs/2610.39026
AB  - The Betke--Henk--Wills conjecture predicts a bound for lattice-point counts in terms of successive minima. Malikiosis introduced the discrete monotonicity property for normalized residue counts as a sufficient condition for this bound and its extension to nonsymmetric convex bodies. We prove that every compact convex set satisfies this property for lattice subgroups of rank at most two, in arbitrary ambient dimension.
ER  -